Electrical Resistance Measurement of an Individual Carbon Nanotube

Aiming at the difficulty in the electrical resistance measurement, we develop a simple statistical model for the carbon nanotubes adequately dispersed in available insulated liquid and introduce the concept of “the most probability”. Based on this model, we obtain the function between macroscopic resistance R and resistance of an individual nanotube, Ro, from which one can calculate the resistance of an individual nanotube by measuring the macroscopic resistance. By computational simulation, we prove the reliability of the model. Then, we analyse the feasibility of the model when applied to experiment.     

软段含羧基的水性聚氨酯物性研究

合成了单官能团小分子物质封端的软硬段皆含羧基的脂环族水性聚氨酯(PU),研究了反离子种类、固含量、外加小分子盐/酸、pH值对水性PU的粘度、粒径、CMC和电导率的影响,同时,比较了不同软段分子量水性PU分散液pH临界值和CMC的差异.实验结果表明,随固含量升高,PU分散液体系粘度增大,当固含量为30wt%时,粘度比固含量20wt%的体系粘度增大约20倍;随小分子盐NaCl的加入,PU分散液电粘滞效应逐渐消失,电导率呈现先减小后增大的趋势,随NaCl的加入/软段分子量提高,PU分散体系的CMC值减小,钙离子对PU粒子扩散双电层的破坏作用更加明显.随pH值的增大,PU分散液体系粒径减小,电导率则升高,随软段分子量提高,pH临界值增大,PU分散体对外加小分子酸存在缓冲作用.     

The bifurcation threshold value of the chaos detection system for a weak signal

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detection system for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detection are correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system for a weak signal is established by using the theory of linear differential equation with periodic coefficients and computing the Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system is defined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of the chaos detection system.     

磁绝缘传输线振荡器中辐射场的非线性行为

 导出了磁绝缘传输线振荡器(MILO)中辐射场的非线性演化方程，并讨论了在临界值点附近可能出现非线性不稳定解的条件。结论是：(1)非线性增长速率与线性增长速率的比值g<1.2，且远离g+γ=1(γ为非线性相位增长率与线性相位增长率的比值)点时，出现非稳定解的失谐量临界值很小，而线性增长速率临界值临界值很大，容易出现非稳定解；(2)当g≥1.2时，任意小的失谐量都可以使场出现非稳定解；(3)线性增长速率越大，越不容易出现非稳定解。     

首次穿过边界概率及其在金融中的应用

本文把数学和管理科学有机结合,为数学应用提出问题,得出新结果,推广了J.Michel Harrison(1985)[1]第43页的命题27,并给出了在金融中的应用.     

非紧集合上的Brezis-Nirenberg定理

本文证明了在非紧集合上的Brezis-Nirenberg定理的结构仍然成立。     

三维自助式类渗流细胞自动机的临界值

本文研究三维自助式类渗流细胞自动机的临界值．得出临界值pc＝0的一些充分条件和必要条件．当pc＞0时，利用定向点渗流的临界值，给出了pc上、下界的显式估计．     

Three-Dimensional Waves in Tilt Thermal Boundary Layers

We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed： the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30° and 64°, it is expected to play an important role in the transition to turbulence.     

CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schrdinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.     

宏观经济分布参数系统的临界值问题

本文把经济系统作为一类生灭过程来考虑 .应用人口控制论和森林系统的成功经验 ,研究经济系统的临界值问题 .首先 ,基于实际的经济分析、预测模型 ,在宏观层次上建立经济系统的控制模型 .连续模型便于理论研究 ,离散模型便于计算机仿真 .然后在这个控制模型的基础上 ,寻找使国民经济持续发展所需要的最小资产积累率表达形式 .本文得到的理论值将帮助我们更深刻地理解经济系统